Ed has been attempting to come up with 4:1 counterexamples using
archers. This is a little bit problematic. Missile combat isn't
really handled realistically in Olympia right now. Missile combat is
one area where you should be able to get more than 4:1 ratio on a
defender -- especially against a large defender like a dragon. But
anyway...

I'm not sure how to choose M and L given these two conditions. Maybe
you can give me some actual numbers (I know you mathematicians hate
that, but my simulator insists on it :-). Certainly in all the
battles I ran, if M/L > 4, the archers win easily. But here are some
examples for N archers + 1 (5000,5000) dragon vs. 10 lions and N
archers + 1 rockthrower, no breaking:

Some of the differences are likely to be statistical abberations, but
at least at the low end there is a real loss of effectiveness by
adding the rockthrower. In 10K trials, -rock 54%, +rock 52%. The
weird thing here is that the 4:1 rule in this case is applying to the
*other* side. The addition of the rockthrower reduces the attack
effectiveness of archer stack, but this doesn't overwhelm the defense
bonus until the archer stack gets a lot of attacks -- which doesn't
happen unless the other side is limited by the 4:1 rule! Strange.

I can try to make this more apparent by beefing up the lions side (to
give the attackers more attack chances). Fighting 25 lions, -rock:
7.76% +rock: 6.33%.

So there you go. There is an extreme case under the 4:1 rule where
adding a certain kind of unit to a stack can make it less effective.